Feshbach Resonances in $p$-Wave Three-Body Recombination within Fermi-Fermi Mixtures of Open-Shell $^{6}\mathrm{Li}$ and Closed-Shell $^{173}\mathrm{Yb}$ Atoms

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Feshbach Resonances in $p$ -Wave Three-Body Recombination within Fermi-Fermi Mixtures of Open-Shell ${}^{6}{Li}$ and Closed-Shell ${}^{173}{Yb}$ Atoms

Alaina Green, Hui Li, Jun Hui See Toh, Xinxin Tang, Katherine C. McCormick, Ming Li, Eite Tiesinga, Svetlana Kotochigova, and Subhadeep Gupta

Phys. Rev. X 10, 031037 – Published 14 August 2020

Abstract

We report on the observation of magnetic Feshbach resonances in a Fermi-Fermi mixture of ultracold atoms with extreme mass imbalance and on their unique $p$ -wave dominated three-body recombination processes. Our system consists of open-shell alkali-metal ${}^{6}{Li}$ and closed-shell ${}^{173}{Yb}$ atoms, both spin polarized and held at various temperatures between 1 and $20 μ K$ . We confirm that Feshbach resonances in this system are solely the result of a weak separation-dependent hyperfine coupling between the electronic spin of ${}^{6}{Li}$ and the nuclear spin of ${}^{173}{Yb}$ . Our analysis also shows that three-body recombination rates are controlled by the identical fermion nature of the mixture, even in the presence of $s$ -wave collisions between the two species and with recombination rate coefficients outside the Wigner threshold regime at our lowest temperature. Specifically, a comparison of experimental and theoretical line shapes of the recombination process indicates that the characteristic asymmetric line shape as a function of applied magnetic field and a maximum recombination rate coefficient that is independent of temperature can only be explained by triatomic collisions with nonzero, $p$ -wave total orbital angular momentum. The resonances can be used to form ultracold doublet ground-state molecules and to simulate quantum superfluidity in mass-imbalanced mixtures.

Received 10 December 2019
Accepted 1 July 2020

DOI:https://doi.org/10.1103/PhysRevX.10.031037

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cold atoms & matter waves Mixtures of atomic and/or molecular quantum gases Scattering theory Ultracold collisions

Atomic, Molecular & Optical

Authors & Affiliations

Alaina Green ^1,*, Hui Li ², Jun Hui See Toh ¹, Xinxin Tang ¹, Katherine C. McCormick¹, Ming Li², Eite Tiesinga ³, Svetlana Kotochigova², and Subhadeep Gupta¹

¹Department of Physics, University of Washington, Seattle, Washington 98195, USA
²Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
³Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA

^*agreen13@uw.edu

Popular Summary

Interacting fermions are the building blocks of matter, from atoms to solids to stars. An improved understanding of the interplay of individual fermions can shed light on complex structures such as superfluids and superconductors, where fermions pair up and give rise to exotic macroscopic behaviors. Here, we experimentally and theoretically study the few-body behavior of a mixture of fermionic atoms of disparate mass and electronic structure under conditions of tunable interaction strength at microkelvin temperatures.

Central to the study is our discovery of tunable interactions in ultracold, trapped mixtures of fermionic closed-shell ytterbium and fermionic open-shell lithium atoms. The tunability is derived from collisional resonances that are accessed via applied magnetic fields. By performing field-dependent spectroscopy on samples with controlled spin composition, our study reveals the underlying spin-coupling mechanism for the resonances. Additionally, we investigate resonant three-body interactions between fermionic isotopes of different elements, demonstrating a characteristic temperature dependence that is a critical consequence of quantum statistics.

We expect that our results will lead to further studies and improved understanding of few- and many-body physics in mass-imbalanced systems and will open the door to the creation of ensembles of ultracold diatomic molecules with an unpaired electron that feature both an electric and a magnetic dipole moment.

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Vol. 10, Iss. 3 — July - September 2020

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Atomic and Molecular Physics

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Figure 1
Three views of the hyperfine and Zeeman energies of ${}^{173}{Yb}$ - ${}^{6}{Li}$ zero-energy scattering and bound states as functions of magnetic field in units of G, where 1 G is 0.1 mT. Panel (a) shows the atomic energies, eigenvalues of $H_{Li} + H_{Yb}$ , by solid blue lines and those of the most weakly bound $s$ -wave bound states, eigenvalues of $H_{0}$ , by dashed red lines. Panel (b) shows an enlargement of the level crossing region near 640 G in (a). Panel (c) is a further enlargement of the crossing region but now shows bound-state energies of $H_{0} + U_{s - i} (R)$ with red dashed lines. Symbols in (b) and (c) mark the level crossings for the MFRs observed in this work. Differences in bound-state energies of Hamiltonians $H_{0}$ and $H_{0} + U_{s - i} (R)$ would only be visible on the scales used in (c).
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Figure 2
Observation of interspecies ${}^{173}{Yb} {}^{6}{Li}$ magnetic Feshbach resonances as functions of magnetic field $B$ . Resonances appear as $B$ -dependent atom loss. The ${}^{6}{Li}$ atom loss is shown after the $2.8 μ K$ mixture has been held for 3 s in the dipole trap. Red squares, purple circles, and blue triangles correspond to data for ${}^{6}{Li}$ in states $| m_{s, Li}, m_{i, Li} ⟩ = | - 1 / 2, 1 ⟩$ , $| - 1 / 2, 0 ⟩$ , and $| - 1 / 2, - 1 ⟩$ , respectively. The nuclear Zeeman state of ${}^{173}{Yb}$ is spin polarized to $| m_{i, Yb} ⟩ = | + 5 / 2 ⟩$ in each case. Each point is the average of at least four measurements and the error bars are one-standard-deviation statistical uncertainties. Curves are best-fit Gaussians and only meant as a guide to the eye. Our full line shape analysis is found in Sec. 7.
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Figure 3
Dependence of magnetic Feshbach resonances on the ${}^{173}{Yb}$ nuclear Zeeman state in a ${}^{173}{Yb}$ - ${}^{6}{Li}$ mixture seen in the remaining ${}^{6}{Li}$ atom number as functions of $B$ near the 640 G Feshbach resonance. ${}^{6}{Li}$ is prepared in hyperfine state $| m_{s, Li}, m_{i, Li} ⟩ = | - 1 / 2, 0 ⟩$ and the ${}^{173}{Yb}$ sample is spin polarized in different nuclear Zeeman states. The data are normalized by the remaining ${}^{6}{Li}$ atom number away from resonance and vertically offset for clarity. The distance between vertical tick marks is one. From top to bottom ${}^{173}{Yb}$ is prepared in nuclear spin state $m_{i, Yb} = - 5 / 2$ , $- 3 / 2$ , $- 1 / 2$ , $+ 1 / 2$ , $+ 3 / 2$ , and $+ 5 / 2$ . No resonance exists for $m_{i, Yb} = - 5 / 2$ . The temperature is $1.8 μ K$ ( $1.0 μ K$ ) for Li (Yb) and the hold time is 1.5 s. Curves are best-fit Gaussians. Our full line shape analysis is found in Sec. 7.
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Figure 4
(a) The observed (pink squares) and theoretically predicted (black circles) resonance locations near $B = 640 G$ as functions of $m_{i, Yb}$ . The ${}^{6}{Li}$ atom is in state $| m_{s, Li}, m_{i, Li} ⟩ = | - 1 / 2, 0 ⟩$ . For better visual comparison, the theoretical values have been uniformly shifted from those shown in Fig. 1. The shift is consistent with the 1.3 G uncertainty in the predicted resonance location. The dashed line is given by Eq. (7). (b) The ${}^{173}{Yb}$ ${}^{6}{Li}$ hyperfine coupling coefficient $ζ_{Yb} (R)$ (solid blue line) and the radial wave function $ϕ^{mol} (R)$ of the most weakly bound state of the ${}^{2}{Σ^{+}}$ potential (solid red line) as functions of separation $R$ . Here, $a_{0} = 0.052 92 nm$ is the Bohr radius.
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Figure 5
Fermionic behavior of three-body recombination processes in ${}^{6}{Li}$ and ${}^{173}{Yb}$ mixtures found in atom-loss spectra and fitted theoretical line shapes as functions of magnetic field. ${}^{6}{Li}$ is prepared in the $| m_{s, Li}, m_{i, Li} ⟩ = | - 1 / 2, 0 ⟩$ state and ${}^{173}{Yb}$ in the $| m_{i, Yb} ⟩ = | + 5 / 2 ⟩$ state. The hold time is 4 s. Panels (a)–(d) correspond to the remaining ${}^{6}{Li}$ atom number normalized to the remaining fitted ${}^{6}{Li}$ atom number away from the resonance (markers with error bars) as a function of $B - B_{0}$ measured at temperatures of ${1.8, 5.8, 9.5, 16.1} μ K$ , respectively. The initial atom numbers for Li (Yb) are ${1.3 (1.0), 1.7 (3.3), 1.3, (2.0), 1.8 (4.0)} \times 10^{5}$ and the initial peak densities for Li (Yb) are ${6.1 (2.6), 12 (8.3), 10 (6.2), 11 (9.3)} \times 10^{12} {cm}^{- 3}$ . The fitted theoretical line shapes are the colored curves. We specify the magnetic field relative to the resonance location $B_{0}$ as determined from the fit. The dash-dotted and dashed lines, where given, locate the fitted resonance location $B_{0}$ and the field of maximum atom loss, respectively. The vertical axes are scaled to the theoretical background values away from the resonance. The magnetic moment of the trimer resonance state is $δ μ_{3} = 2.8 μ_{B}$ , while $B_{0} = 640.476$ G, $A / k_{B} = 6 \times 10^{- 6} nK$ , and $Γ_{br} / k_{B} = 100 nK$ . The one-body loss rate is $Γ_{bg} = 0.1 s^{- 1}$ for our lowest temperature and $0.075 s^{- 1}$ otherwise. Panel (e) shows the theoretical event rate coefficients as functions of $B - B_{0}$ for our four temperatures. The line colors correspond to those used in (a)–(d).
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Physical Review X

Feshbach Resonances in p-Wave Three-Body Recombination within Fermi-Fermi Mixtures of Open-Shell Li6 and Closed-Shell Yb173 Atoms

Alaina Green, Hui Li, Jun Hui See Toh, Xinxin Tang, Katherine C. McCormick, Ming Li, Eite Tiesinga, Svetlana Kotochigova, and Subhadeep Gupta

Phys. Rev. X 10, 031037 – Published 14 August 2020

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Feshbach Resonances in $p$ -Wave Three-Body Recombination within Fermi-Fermi Mixtures of Open-Shell ${}^{6}{Li}$ and Closed-Shell ${}^{173}{Yb}$ Atoms